# Sine Rule Problems

**Problem 1** In the ABC we have AB = 30cm and γ = 45°. Find the length of the radius of the perscribed circumference.

Answer: 15√2cm.

**Problem 2** The radius of the perscribed around ABC circumference is R = 2√3/3cm. Find the size of the angle α, if BC = 2cm.

Answer: 60°.

**Problem 3** In the ABC α : β : γ = 1 : 3: 8. Find the length if the side AC, if AB = 10cm.

Answer: 10√63cm.

**Problem 4** In the circumference with radius 7cm, the arc AB is 120°. Find the chord AB.

Answer: 7√3cm.

**Problem 5** In the isosceles triangle ABC, the base AB = 12cm, and the angle at the top is 30°. On the hip BC is taken point D so that CAD : DAB = 1 : 4. Find the length of the radius of the perscribed circumference around the ABD.

Answer: 6√2cm.

**Problem 6** The base of isosceeles triangle is 10cm, and the anlge at the base is 2α. Find the bisectrice of the angle at the base.

Angle: 10sin2α/sin3α.

**Problem 7** In the ABC we have AB = 12cm and γ = 60°. Find the radius of the perscribed around the ABL circumference, if the point L is the L intersect of the bisectrices of ABC.

Answer: 4√3cm.

**Problem 8** In the circumference with radius 50cm is inscribed quadrilateral. Two if its angles are 45° and 120°. Find the diagonales.

Answer: 50√2cm or 50√3cm.

**Problem 9** In ABC we have α = 45°, β = 30°. On the side AB we is chosen point M. The radius of the perscribed around the AMC circumference is R. Find the radius of the perscribed around the MBC circumference.

Answer: R√2cm.